Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants

DOI10.1016/0096-3003(88)90030-6zbMath0651.65058OpenAlexW1995491944MaRDI QIDQ1106630

Syvert P. Nørsett, W. H. Enright, Kenneth R. Jackson, Per Grove Thomsen

Publication date: 1988

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(88)90030-6

zbMATH Keywords

Numerical examplesprogramsRunge-Kutta formuladiscontinuous initial-value problemslocal interpolants

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items

A new error-control for initial value solvers ⋮ An efficient IMEX method for nonlinear functional differential equations with state-dependent delay ⋮ A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side ⋮ Dense output for extrapolation methods ⋮ Multivalue collocation methods free from order reduction ⋮ A finite difference approach for the numerical solution of non-smooth problems for boundary value odes ⋮ Rosenbrock-type methods applied to discontinuous differential systems ⋮ Numerical computation of derivatives in systems of delay differential equations ⋮ Error control for initial value problems with discontinuities and delays ⋮ Numerical solution of differential-algebraic equations in mechanical systems simulation ⋮ Pulse detection software for initial value ODEs ⋮ Integrating Lipschitzian dynamical systems using piecewise algorithmic differentiation ⋮ Runge-Kutta research at Toronto ⋮ Recent trends in the numerical solution of retarded functional differential equations ⋮ Event location for ordinary differential equations ⋮ Continuous numerical methods for ODEs with defect control ⋮ Open issues in devising software for the numerical solution of implicit delay differential equations ⋮ Runge-Kutta Methods for Differential Equations with Variable Time of Impulses

Uses Software

• dverk

Cites Work

• One-step methods of any order for ordinary differential equations with discontinuous right-hand sides
• Solving Ordinary Differential Equations with Discontinuities
• Practical Aspects of Interpolation in Runge-Kutta Codes
• A Theoretical Criterion for Comparing Runge–Kutta Formulas
• Interpolants for Runge-Kutta formulas